Which of the following equations is dimensionally incorrect?
Where $\mathrm{t}=$ time, $\mathrm{h}=$ height, $\mathrm{s}=$ surface tension, $\theta=$ angle,$\rho=$ density, a, $r=$ radius, $\mathrm{g}=$ acceleration due to gravity, $\mathrm{v}=$ volume, $\mathrm{p}=$ pressure, $\mathrm{W}=$ work done, $\Gamma=$ torque, $\in=$ permittivity, $\mathrm{E}=$ electric field, $\mathrm{J}=$ current density, $\mathrm{L}=$ length.
$\mathrm{v}=\frac{\pi \mathrm{pa}^{4}}{8 \eta \mathrm{L}}$
$\mathrm{h}=\frac{2 s \cos \theta}{\rho \mathrm{rg}}$
$\mathrm{J}=\epsilon \frac{\partial \mathrm{E}}{\partial \mathrm{t}}$
$\mathrm{W}=\Gamma \theta$
Correct Option: 1
(i) $\frac{\pi \mathrm{pa}^{4}}{8 \eta \mathrm{L}}=\frac{\mathrm{dv}}{\mathrm{dt}}=$ Volumetric flow rate
(poiseuille's law)
(ii) $\mathrm{h} \rho \mathrm{g}=\frac{2 \mathrm{~s}}{\mathrm{r}} \cos \theta$
(iii) $\mathrm{RHS} \Rightarrow \varepsilon \times \frac{1}{4 \pi \varepsilon_{0}} \frac{\mathrm{a}}{\mathrm{r}^{2}} \times \frac{1}{\varepsilon}=\frac{\mathrm{q}}{\mathrm{t}} \times \frac{1}{\mathrm{r}^{2}}$
$=\frac{\mathrm{I}}{\mathrm{L}^{2}}=\mathrm{IL}^{-2}$
LHS
$\mathrm{T}=\frac{\mathrm{I}}{\mathrm{A}}=\mathrm{IL}^{-2}$
(iv) $\mathrm{W}=\tau \theta$
Option (1)
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All Study Material
- JEE Main
- Exam Pattern
- Previous Year Papers
- PYQ Chapterwise
- Physics
- Kinematics 1D
- Kinemetics 2D
- Friction
- Work, Power, Energy
- Centre of Mass and Collision
- Rotational Dynamics
- Gravitation
- Calorimetry
- Elasticity
- Thermal Expansion
- Heat Transfer
- Kinetic Theory of Gases
- Thermodynamics
- Simple Harmonic Motion
- Wave on String
- Sound waves
- Fluid Mechanics
- Electrostatics
- Current Electricity
- Capacitor
- Magnetism and Matter
- Electromagnetic Induction
- Atomic Structure
- Dual Nature of Matter
- Nuclear Physics
- Radioactivity
- Semiconductors
- Communication System
- Error in Measurement & instruments
- Alternating Current
- Electromagnetic Waves
- Wave Optics
- X-Rays
- All Subjects
- Physics
- Motion in a Plane
- Law of Motion
- Work, Energy and Power
- Systems of Particles and Rotational Motion
- Gravitation
- Mechanical Properties of Solids
- Mechanical Properties of Fluids
- Thermal Properties of matter
- Thermodynamics
- Kinetic Theory
- Oscillations
- Waves
- Electric Charge and Fields
- Electrostatic Potential and Capacitance
- Current Electricity
- Thermoelectric Effects of Electric Current
- Heating Effects of Electric Current
- Moving Charges and Magnetism
- Magnetism and Matter
- Electromagnetic Induction
- Alternating Current
- Electromagnetic Wave
- Ray Optics and Optical Instruments
- Wave Optics
- Dual Nature of Radiation and Matter
- Atoms
- Nuclei
- Semiconductor Electronics: Materials, Devices and Simple Circuits.
- Chemical Effects of Electric Current,